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Preface to PerspectivesIn 2004 theAIChE Journalcelebrated its 50th anniversary. In connection with this milestone, a symposium on The Future of Chemical

Engineering Research was organized at the Annual AIChE Meeting in Austin. The symposium consisted of three sessions entitled: Fundamentals Biological Engineering Complex Systems

In each session seven talks by leading chemical engineers were followed by a three-member panel discussion. A one-person

overview that integrated the talks and discussions within the context of our disciplines research tradition closed the proceedings.

The symposium proved an excellent opportunity for taking a broad look at the current landscape of chemical engineering

research, and for thinking about its future. It is clearly impossible to organize three sessions that can provide a comprehensive

representation of every important aspect of chemical engineering research. Nevertheless, we believe that the scope and quality of

the talks were such that it is of value to our profession to preserve a written record of the symposium. We are delighted that the

AIChE Journal will be the medium for its publication.

This issue of the AIChE Journal features the third collection of Perspective articles dedicated to the 2004 Symposium The

Future of Chemical Engineering Research. The three articles in this issue correspond to the session on Biological Engineering.The session on Complex Systems appeared in July, and the series of Fundamentals Perspectives appeared in the September issue.

We are grateful to the many speakers who were able to contribute to this collection by putting their talks and thoughts on paper.

We feel honored and privileged to have organized the symposium and to edit this collection of papers. The program of the session

on Biological Engineering is reproduced below.

Arup K. Chakraborty, Pablo G. Debenedetti, Julio M. Ottino

The Future of Chemical Engineering Research

November 8, 2004

AIChE Annual Meeting, AUSTIN, TX

SESSION II: BIOLOGICAL ENGINEERING

Arup Chakraborty, Chair; University of California-BerkeleyPablo Debenedetti, co-Chair; Princeton University

Materials For Drug DeliveryMark E. Davis, California Institute of Technology

Metabolic Engineering of Bacteria for Drug ProductionJay D. Keasling, University of California-Berkeley

Entropy, Disease, and New Opportunities for Chemical Engineering ResearchMichael W. Deem, Rice University

Protein Engineering and Biopharmaceutical DesignK. Dane Wittrup, M.I.T.

Biomaterials in Regenerative Medicine: Future ThrustsKristi Anseth, University of Colorado-Boulder

Developing Pharmaceutical ProductsMauricio Futran, Bristol, Myers, Squibb

Intercellular Communication in the Adaptive Immune System: Plenty of Room at the BottomArup Chakraborty, University of California-Berkeley

Summary and Discussion

George Georgiou (University of Texas, Austin)

Daniel A. Hammer (University of Pennsylvania)

Gregory Stephanopoulos (MIT)

AIChE Journal, Vol. 51, 3082 (2005) 2005 American Institute of Chemical EngineersDOI 10.1002/aic.10728PublishedonlineOctober 28,2005 in WileyInterScience (www.interscience.wiley.com).

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THE FUTURE OF CHEMICAL ENGINEERINGRESEARCH: BIOLOGICAL ENGINEERING

Directed Evolution in Chemical Engineering

K. Dane WittrupDept. of Chemical Engineering and Division of Biological Engineering, Massachusetts Institute of Technology,

MIT 66-552, Cambridge, MA 02139

Entropy, Disease, and New Opportunities forChemical Engineering Research

Michael W. DeemRice University, 6100 Main Street-MS 142, Houston, TX 77005

Metabolic Engineering: Developing NewProducts and Processes by Constructing

Functioning Biosynthetic Pathwaysin vivo

Gregory Stephanopoulos and Kyle L. JensenMassachusetts Institute of Technology, Dept. of Chemical Engineering 77 Massachusetts Avenue, Cambridge, MA 02137

Perspectives

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Directed Evolution in Chemical Engineering

K. Dane Wittrup

Dept. of Chemical Engineering and Division of Biological Engineering, Massachusetts Institute of Technology,MIT 66-552, Cambridge, MA 02139

DOI 10.1002/aic.10706

Published online October 4, 2005 in Wiley InterScience (www.interscience.wiley.com).

Keywords: directed evolution, protein engineering, molecular bioengineering

Predictions are hard to make, especially about the future. Niels Bohr, and Yogi Berra

A role for prediction?

Top-down exercises in research area prognostication of-

ten miss the mark. The most general predictions can beplatitudinously unfalsifiable; the most specific are often

amusingly wrong in retrospect. Given the primacy of investi-

gator-initiated efforts in the successful definition and exploita-

tion of new research areas, it is fair to question the utility of

the future of. . . pieces, such as this one.

I well recall sitting through keynote presentations by eminent

senior colleagues in the biochemical engineering field at national

meetings in the late 1980s and early 1990s, the tenor of which was

that the essential premise of my research program was an enor-

mous mistake, straying too far from the hard ChE core. A partic-

ularly memorable assertion was that It is better to be a first-rate

chemical engineer than a second-rate biologist. (Fortunately

these do not appear to be the only two available options.) Edito-rializing is an ineffective means of squelching initiative, by com-

parison to the ruthless efficiency of the existing marketplace of

ideas. Successful research directions are determined, over a suf-

ficient time span, by peer-reviewed funding and publication, the

interest of new students, and the willingness of academia and

industry to hire students trained to perform such research. If

exercises such as this one are capable of serving a useful purpose,

perhaps it is to constructively recognize incipient grass-roots

movements and highlight exciting challenges.

Synthesis in Chemical Engineering

A shift from process to product engineering within ChE hasbeen noted previously, and has been embraced systemically in

U.S. academic departments. Synthetic capabilities are an es-

sential tool for invention, as evidenced by numerous accom-

plishments of ChE researchers applying and developing syn-

thetic tools in the fields of electronic materials, polymers,

MEMS devices, and drug delivery. A new opportunity for ChE

contributions beckons with the explosive growth in the devel-

opment of protein biopharmaceuticals. Proteins play a central

role in biological function and many pathologies. The thera-

peutic efficacy of a protein drug is inextricably linked to its

binding properties, and consequently tools for engineering pro-

tein binding are indispensable, as well as analytical tools to

properly determine biophysical design criteria.1

At present the most powerful and robust approach to engi-

neering protein properties is Directed Evolution, and the field

of chemical engineering has quietly gone about becoming the

predominant academic home for Directed Evolution research.

A cursory examination of departmental web sites reveals over

20 ChE faculty in the U.S. (most of whom began their careers

in the past 15 years) whose research programs are extensively

dedicated to developing or using Directed Evolution. Combi-

natorial polypeptide library screening consists of a series of

equilibrium and/or transient biochemical transformations that

are well suited to analysis with classical chemical reaction

engineering tools.2-5 Widely-practiced innovations in proteinscreening methodology have originated from ChE research

groups.6-8 The fundamental structure of the fitness landscape,

and improved search methods for it, has been a fruitful source

for interesting research problems.9-14 A growing direction is the

use of chemical engineering analyses to guide the development

of optimized protein biopharmaceuticals.1, 15-19 In terms of

analytical contributions, cellular signaling pathways,20, 21 me-

tabolism,22, 23 and immunology24, 25 hold tremendous promise

for chemical engineers, and these approaches are likely to

contribute to rationalization of protein drug pharmacology.

Curricular development in chemical and biologicalengineering

There has been a significant level of angst in the ChE commu-

nity with respect to the Whitaker-driven expansion of academic

biomedical engineering programs, with concomitant reductions in

ChE undergraduate enrollments. However, allowing the ChE cur-

riculum to be driven by the actions of external communities is

existentially unsatisfying and unlikely to be a recipe for innovation.

At the risk of Pollyanna optimism, the ChE discipline is in a

very strong position on the ground with respect to biomolecular

engineering. If the ChE analytical toolkit did not exist, it would

be necessary to invent it in order to solve many of the problems

in modern bioengineering. Critical foundations of biomolecular

processes are the rates of biochemical conversions and their

K. D. Wittrups e-mail address is [email protected].

2005 American Institute of Chemical Engineers

Perspective



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equilibria, and the rates of biomolecular movement by diffu-

sion and convection. The ChE triumvirate core of kinetics,

thermo, and transport are the required tools for such analyses.

Although BME curricula generally include transport course-

work, BME training programs in general do not incorporate

kinetics and chemistry to the extent necessary for modern

biomolecular engineering.

ChE should not rest on its laurels, however; incorporating

biology into the ChE curriculum is not so simple as adding afew new examples or homework problems, because there are

new intellectual principles from biochemistry, biophysics, and

cell biology that must be integrated throughout the toolkit. The

most effective means for syllabus evolution will be to staff

courses with champions dedicated to change; given the large

numbers of young ChE faculty with biological interests now

disseminated throughout the U.S., this is already occurring.

These efforts will be amplified by the emergence of new

textbooks incorporating biological principles in an integrated

fashion rather than grafted onto existing outlines.

Precis and outlook

There are an extraordinary number of significant opportuni-ties in biomedicine to engineer proteins by directed evolution. 1,

26-28 Many chemical engineers have recognized this opportu-

nity and are exploiting it with vigor, making chemical engi-

neering the academic center of mass for the burgeoning field of

Directed Evolution.

Literature Cited

1. Rao BM, Lauffenburger DA, Wittrup KD. Integrating cell-

level kinetic modeling into the design of engineered pro-

tein therapeutics. Nat Biotechnol. 2005;23(2):191-4.

2. Maheshri N, Schaffer DV. Computational and experimen-

tal analysis of DNA shuffling. Proc Natl Acad Sci U S A.

2003;100(6):3071-6.

3. Daugherty PS, Olsen MJ, Iverson BL, Georgiou G. Devel-

opment of an optimized expression system for the screen-

ing of antibody libraries displayed on the Escherichia coli

surface. Protein Eng. 1999;12(7):613-21.

4. Boder ET, Wittrup KD. Optimal screening of surface-dis-

played polypeptide libraries.Biotechnol Prog. 1998;14(1):55-

62.

5. Moore GL, Maranas CD. Modeling DNA mutation and

recombination for directed evolution experiments. J Theor

Biol. 2000;205(3):483-503.

6. Zhao H, Giver L, Shao Z, Affholter JA, Arnold FH. Molec-

ular evolution by staggered extension process (StEP) in vitro

recombination.Nat Biotechnol. 1998;16(3):258-61.7. Francisco JA, Earhart CF, Georgiou G. Transport and anchor-

ing of beta-lactamase to the external surface of Escherichia

coli.Proc Natl Acad Sci U S A. 1992;89(7):2713-7.

8. Boder ET, Wittrup KD. Yeast surface display for screen-

ing combinatorial polypeptide libraries. Nat Biotechnol.

1997;15(6):553-7.

9. Voigt CA, Mayo SL, Arnold FH, Wang ZG. Computational

method to reduce the search space for directed protein evo-

lution.Proc Natl Acad Sci U S A. 2001;98(7):3778-83.

10. Moore GL, Maranas CD. Identifying residue-residue clashes

in protein hybrids by using a second-order mean-field ap-

proach.Proc Natl Acad Sci U S A. 2003;100(9):5091-6.

11. Bogarad LD, Deem MW. A hierarchical approach to pro-

tein molecular evolution. Proc Natl Acad Sci U S A.

1999;96(6):2591-5.

12. Earl DJ, Deem MW. Evolvability is a selectable trait.Proc

Natl Acad Sci U S A. 2004;101(32):11531-6.

13. Daugherty PS, Chen G, Iverson BL, Georgiou G. Quanti-

tative analysis of the effect of the mutation frequency on

the affinity maturation of single chain Fv antibodies. Proc

Natl Acad Sci U S A. 2000;97(5):2029-34.

14. Drummond DA, Iverson BL, Georgiou G, Arnold FH.

Why high-error-rate random mutagenesis libraries are en-

riched in functional and improved proteins. J Mol Biol.

2005;350(4):806-16.

15. Graff CP, Wittrup KD. Theoretical analysis of antibody

targeting of tumor spheroids: importance of dosage for

penetration, and affinity for retention. Cancer Res. 2003;

63(6):1288-96.

16. Sarkar CA, Lauffenburger DA. Cell-level pharmacokinetic

model of granulocyte colony-stimulating factor: implica-

tions for ligand lifetime and potency in vivo. Mol Phar-

macol. 2003;63(1):147-58.

17. Rao BM, Driver I, Lauffenburger DA, Wittrup KD. High-Affinity CD25-Binding IL-2 Mutants Potently Stimulate Per-

sistent T Cell Growth.Biochemistry. 2005;44(31):10696-701.

18. Haugh JM. Mathematical model of human growth hor-

mone (hGH)-stimulated cell proliferation explains the ef-

ficacy of hGH variants as receptor agonists or antagonists.

Biotechnol Prog. 2004;20(5): 1337-44.

19. Kim JR. Gibson TJ, Murphy RM. Targeted control of kinetics

of beta-amyloid self-association by surface tension-modify-

ing peptides.J Biol Chem. 2003;278(42):40730-5.

20. Kao KC, Yang YL, Boscolo R, Sabatti C, Roychowdhury

V, Liao JC. Transcriptome-based determination of multi-

ple transcription regulator activities in Escherichia coli by

using network component analysis. Proc Natl Acad Sci US A. 2004;101(2):641-6.

21. Sachs K, Perez O, Peer D, Lauffenburger DA, Nolan GP.

Causal protein-signaling networks derived from multipa-

rameter single-cell data. Science. 2005;308(5721):523-9.

22. Price ND, Reed JL, Palsson BO. Genome-scale models of

microbial cells: evaluating the consequences of con-

straints. Nat Rev Microbiol. 2004;2(11):886-97.

23. Alper H, Miyaoku K, Stephanopoulos G. Construction of

lycopene-overproducing E. coli strains by combining sys-

tematic and combinatorial gene knockout targets. Nat Bio-

technol. 2005;23(5):612-6.

24. Chakraborty AK. Decoding communications between cells

in the immune system using principles of chemical engi-neering. AIChE J. 2003;49(7):1614-1620.

25. Munoz ET, Deem MW. Epitope analysis for influenza

vaccine design. Vaccine. 2005;23(9):1144-8.

26. Brekke OH, Sandlie I. Therapeutic antibodies for human

diseases at the dawn of the twenty-first century. Nat Rev

Drug Discov. 2003;2(1):52-62.

27. Vasserot AP, Dickinson CD, Tang Y, Huse WD, Manchester

KS, Watkins JD. Optimization of protein therapeutics by

directed evolution. Drug Discov Today. 2003;8(3):118-26.

28. Lazar GA, Marshall SA, Plecs JJ, Mayo SL, Desjarlais JR.

Designing proteins for therapeutic applications.Curr Opin

Struct Biol. 2003;13(4):513-8.



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Entropy, Disease, and New Opportunities for

Chemical Engineering ResearchMichael W. Deem

Rice University, 6100 Main Street-MS 142, Houston, TX 77005

DOI 10.1002/aic.10718


Keywords: influenza, bird flu, cancer, autoimmune disease

Executive Summary

Randomness, diversity, fluctuations, and correlationsplay a significant role in disease, disease treatment, andthe immune response to disease. I suggest that statistical

mechanics, the physical theory of randomness that uses asystems physical behavior at the molecular or atomic scale tosynthesize a picture of the behavior at a larger level, canaddress some of these issues. Theory and mathematical mod-eling can help design or redesign treatment strategies. Theorycan also help determine what makes redesign necessary. Idescribe three lines of research in my group seeking this newmathematics of biology.

Efficacy of the Influenza Vaccine TheResponse of the Immune System to aPerturbation

Influenza epidemics are annually responsible for the deathsof 25,0000 to 50,0000 people in the world and cause illness in5 to 15% of the total population each year (World HealthOrganization, 2003). The total cost associated with influenza inthe U.S. is roughly $10 billion (Lave et al., 1999), and theeconomic cost of an influenza pandemic has been estimated tobe $71167 billion (Meltzer et al., 1999) in the U.S. alone. Theprimary method employed to prevent infection by influenzaand its associated complications is vaccination. Mutation and

antigenic change, combined with the high rate of transmissionof influenza strains, means that the vaccine must be redesignedeach year. This is currently done with phylogenetic, animalmodel, and epidemiological analysis.

The effectiveness of the influenza vaccine varies each yeardue to changes in the molecular structure of the influenzastrains that are circulating. Three strains are customarily in-cluded in the annual influenza vaccine, with these three strainschosen to be as similar as possible to those estimated to be the

most widespread circulating strains in the upcoming flu season.

Currently, the vaccine contains a H3N2 and a H1N1 influenzaA component and an influenza B component. Due to mutationof the influenza virus, vaccine efficacy is rarely 100%, and ismore typically 30 60%, against influenza-like illness. Theestimated worldwide mortality rises by another 160%260% ifinfluenza-induced complications in patients with other condi-tions are included (Neuzil et al., 1999; Sprenger et al., 1993).It is believed that the influenza vaccine, on average, signifi-cantly reduces such excess mortality (Hak et al., 2002). Vac-cine efficacy can be negative, however, due to original anti-genic sin (Davenport et al., 1953; Fazekas de St. Groth andWebster, 1966; Deem and Lee, 2003), which is the tendencyfor antibodies produced in response to exposure to one influ-

enza vaccine antigen to suppress the creation of new, differentantibodies in response to exposure to a new version of theinfluenza virus. The efficacy of the annual influenza vaccine,and whether original antigenic sin occurs, depends delicatelyon the similarity between the vaccine and circulating viralstrains. The current standard of practice is to measure antigenicdistance by ferret antisera hemagglutinin inhibition assays(Smith et al., 2004; Smith et al., 1999; Lee and Chen, 2004),and these distances have been assumed to correlate well withvaccine efficacies in humans. However, to my knowledge nosuch significant correlation has ever been shown for an exper-imental, animal model, or theoretical measure of antigenicdistance. Besides being useful for the annual flu shot design, a

reliable measure of antigenic distance would help to stem thespread of a newly emerged influenza strain by allowing forstreamlined decision making if preparation and rush productionof a modified vaccine is necessary (Ault, 2003).

So, what is the best order parameter to describe antigenicdistance, and which also correlates well with vaccine efficacy?Using the tools of statistical mechanics, we provided a quan-titative definition of the difference between the dominantepitope regions in the vaccine and circulating strain, ppeptide(Deem and Lee, 2003; Gupta et al., 2005). We showed that thisdefinition of antigenic distance correlates well with humaninfluenza vaccine efficacy over the past 35 years (see Figure 1)(Munoz and Deem, 2005; Gupta et al., 2005).

M. W. Deems e-mail address is [email protected].


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A different and highly lethal strain of influenza, the H5N1 avianinfluenza strain, was first detected in humans in Hong Kong in1997 (Saw et al., 1998; Claas et al., 1998). Since then, it hasspread to at least eight other Asian countries (Normile andEnserink, 2005; Cyranoski, 2005a), and Russia (Allakhverdov andEnserink, 2005), and it is widely expected to enter the rest ofEurope through migrating birds. To date there have been roughly60 reported deaths due to the H5N1 strain. The initial mortality of70% decreased to roughly 20% (Normile, 2005b), which suggeststhe bird flu is evolving to become less fatal but concurrently moreable to persist and, thus, to create an epidemic. Avian influenzahas also been observed in pigs, a classic mixing vessel for influ-enza (Cyranoski, 2005b). Person-to-person transmission has beensuggested (Ungchusak et al., 2005). Avian influenza is, thus,evolving (Normile, 2005a; Hulse-Post et al., 2005). Vaccines,antivirals, animal culling, and public health measures (Longini etal., 2005; Ferguson et al., 2005) are the main weapons againstspread of the bird flu. Various countries are stockpiling bird fluvaccines, and a vaccine produced from one test strain of the birdflu has produced an immune response in healthy adults (WorldHealth Organization, 2005). However, since the bird flu is mutat-ing, which strains should be stockpiled? The National Institute ofAllergy and Infectious Disease is making sequences of the H5strains available (Kaiser and Vogel, 2004). The U.S. Centers for

Disease Control and Prevention are, controversially, investigatingthe potential reassortments of the bird flu that might create anepidemic (Khamsi, 2005). However, the key question remains:What is the required or optimal diversity of vaccine stockpile? Inparticular: How cross-protective will a bird flu vaccine be againstother strains that exist or will evolve into existence? The extent ofcross-protection is needed to determine the optimal vaccines tostockpile and how to administer them (Patel et al., 2005).

To protect against the strains observed to date, how manyvaccine components are needed? We used results from data(Gupta et al., 2005) and theory (Deem and Lee, 2003) of theinfluenza vaccine effectiveness to estimate how cross-protectivethe bird flu vaccine will be (Zhou and Deem, 2005). We used the

50 strains of H5N1 observed to date (Macken et al., 2001) tocharacterize the diversity of a typical pandemic. While vaccinesagainst typical influenza A strains contain only the dominantstrain, as subdominant strains typically last only a few seasons(Fitch et al., 1997), a bird flu pandemic may well be over in oneseason. There may be significant mortality from multiple strains,and so protection against all strains may be important. We con-sidered that the vaccine will contain only those strains that have

been observed in the wild, due to the ethical questions arising fromdeveloping and vaccinating with mutant strains. We examined allcombinations of the wild-type strains, searching for the combina-tion with the least number of components. To cover all thesestrains with at least 15% vaccine efficacy, we predicted that 3vaccine strains would be needed.

Evolution of the H5N1 strain may well render existing vaccinestockpiles ineffective, and public health authorities may have todepend almost completely on the production of new vaccinestrains, in addition to antivirals, animal culling, and quarantine.The value of pepitope can be used to estimate the expectedefficacy of vaccine stockpiles and, thus, to decide whether todeploy them. Our results suggest that reverse genetics or DNA-

based vaccines, both able to rapidly deploy a new vaccine, will beuseful in the prevention of wide-spread infection during an H5N1epidemic given the slow and unreliable nature of the traditionalvaccine production in hens eggs. Thus, a chemical engineeringapproach may contribute not only to the vaccine design, but alsoto the production (Khosla, 2002).

Evolution in Antibody Sequence Space andAutoimmune Disease

The immune system normally protects the human host againstdeath by infection. The immune system tends to produce antibod-ies with binding constants of at most 106 - 107 l/mol. Experimen-tally, however, it is possible to find binding constants betweenantibodies and substrates on the order of 1011 1013 l/mol(Schier et al., 1996), and the laboratory techniques to find theseantibodies (Maynard and Georgiou, 2000; Swers et al., 2004)mimic mechanisms that exist within the natural hierarchy ofevolutionary events (Kidwell and Lisch, 2001; Earl and Deem,2004). The method that the immune system uses to search se-quence space is rather slow the same mechanisms that can findantibodies with higher affinity can also find them more quickly.Thus, one would think that these more powerful evolutionarymechanisms would give an immune system that responds fasterand more effectively against disease. So, why didnt we evolvethat kind of adaptive response?

To answer this question, we first sought to understand theevolutionary rules that govern the way the immune system re-sponds to an infection. With that framework in place, we identifieda biologically-plausible strategy that would allow the immunesystem to react more quickly and with more effective antibodies.Our analysis revealed that such a system would be about 1,000times more likely to produce antibodies that attack healthy tissues(See Figure 2) (Sun et al., 2005). Such cross reactivity due toincreased affinity has recently been observed (Holler et al., 2003).

Antibodies that bind with a molecule other than the antigen theyevolved to attack are called cross-reactive, and cross-reactivity cancause autoimmune disease. For example, chronic infection hasbeen found to be correlated with increased probability of autoim-

Figure 1. Vaccine efficacy for influenza-like illness as a

function of pepitope as observed in epidemio-

logical studies and as predicted by theory.

Also shown is a linear least squares fit to the data (longdashed, R2 0:81). From (Gupta et al., 2005).



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mune disease (Leirisalo-Repo, 2005; Kaplan et al., 1997). How-ever, the strength and significance of this correlation is controver-sial (Carty et al., 2003). Our model suggests a broad distributionfor the time of onset of autoimmune disease due to chronicinfection. Researchers have been looking for a clear, significantcorrelation in time, but a long distribution of onset times wouldlead to weaker statistical correlations, particularly in those caseswhere the infection persisted the longest. Searching for this dis-tribution could elucidate this immunological puzzle and settle thescientific controversy.

We found that the human immune system evolved to mini-mize the risk of cross-reactivity. For example, each cell in ourbodies contains about 100,000 proteins with an average of 500amino acids apiece. Consequently, there are about 1012 poten-tial docking sites, or epitopes, where antibodies could mistak-enly attach themselves to proteins in a healthy cell. The mu-tation response method employed by our adaptive immune

system seems keyed to this number, producing antibodies thatare statistically likely to mistakenly bond with healthy proteinsslightly less than one in 1012 times, meaning that on average,they recognize only invading pathogens.

Randomness of Cancer

The percentage of Americans dying from cancer is thesame as what it was in 1970. . . and the same as what it wasin 1950 (Leaf, 2004). Although some progress has beenmade, especially for childhood cancers, cancer remains alargely unsolved purge of modern society. Mouse modelsremain largely unpredictive, and cancer seems a tremen-

dously complicated disease. Heterogeneity and randomnessare two factors that distinguish cancer from other, more

treatable diseases. New fundamental concepts are desper-ately needed in the fight against cancer.

I suggest that the tools of statistical mechanics, the physicaltheory of randomness, may provide a conceptual frameworkfor cancer drug and vaccine discovery. The design of thera-

peutic cancer vaccines to effectively besiege a cancer epitope isa pivotal piece of the current war on cancer. Indeed, a molec-

ular-level understanding of cancer is vital to develop muchneeded diagnostic and therapeutic tools. Thus, the immune

response to cancer vaccines must be dissected at the molecularbiophysics level.

Several features of cancer and the immune system limit theeffectiveness of traditional vaccination techniques (Dunn et al.,

2002; Schreiber et al., 2002; Whelan et al., 2003). In light ofthe need to deliver multiple, related vaccines to eradicate acancer (Stuge et al., 2004; Whelan et al., 2003; Markiewicz and

Kast, 2004), a multisite vaccination strategy appears promising(Schreiber et al., 2002). In my group, we developed a quanti-

tative theory that explains the success of the new multisiteapproach (see Figure 3), and we are using this theory use to

guide the arduous process of vaccine design (Yang et al.,2005). By inducing a T cell response to each cancer-associatedepitope in a distinct lymph node, vaccine efficacy is increased,

and immunodominance is reduced. The approach captures therecognition characteristics between the T-cell receptors

(TCRs), and tumor, the primary dynamics due to TCR resourcecompetition (Kedl et al., 2003), and the secondary dynamicsdue to competition between escape of tumor cells by epitope

mutation and allele loss, and elimination of tumor cells byTCRs. This approach may be applied to both solid tumors andpost-surgical micrometastases.

Sculpting the diversity of the TCR repertoire is a means toreduce immune evasion of tumor cells due to epitope mutation or

MHC I allele loss. The TCR diversity provides a recognitionreserve to target the unmutated, subdominant epitopes (Nikolich-Zugich et al., 2004). The importance of diversity, the biological

analog of entropy in this problem, is naturally appreciated withinthe context of statistical mechanics.

The solid nature of tumors presents some challenges to immune

control, but also some opportunities for engineering contributions.It may be difficult, for example, for T cells to enter the solidtumor. Conversely, high intensity focused ultrasound can disrupt

solid tumors and can enhance systemic antitumor cellular immu-nity (Wu et al., 2004). Although the exact mechanism of this

enhancement is unknown, one possibility is that the fragments oftumor after destruction can travel to different lymph nodes and,thus, induce a diverse TCR repertoire, in similar fashion to poly-

topic vaccination. More prosaically, the physical disruption of thetumor can allow easier entry of the T cells. Another feature ofsolid tumors is the enhanced probability of uptake of large pro-

teins, due to the highly porous capillaries in tumors (Raucher andChilkoti, 2001). By using this property, stimulants of T cell

activity may be localized to the tumors. The concentration of suchstimulants could be increased further by conjugation with elastin-like polypeptides that undergo a thermally triggered phase transi-

tion in heated tumors, causing selective aggregation in the tumor(Raucher and Chilkoti, 2001).

Figure 2. Affinity of memory antibody sequences after a

primary immune response for the two different

immune system strategies (PM and GSSPM)

to altered antigens.

The binding constant is K, and the antigenic distance of thenew altered antigen from the original antigen is p. Cross-reactivity ceases at larger distances in the GSSPM case (nocross-reactivity for p 0:472) than in the PM only case (nocross-reactivity for p 0:368). Theory shows that theseresults imply the antibodies evolved by the GSSPM dynam-ics will recognize on average 103 more epitopes than theantibodies evolved by the PM dynamics alone. From (Sun etal., 2005).



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Summary

By a discussion of three examples, I hope to have convinced thereader that significant unsolved theoretical problems exist in med-icine and that statistical mechanics has a pivotal role to play in

their solution. The importance of randomness to the proper func-tioning of the immune system seems an especially ripe topic forstatistical mechanical analysis. Many, if not most, problems inimmunological diversity remain open, and identification of themodels and theories to tackle these problems is just starting.Interaction with immunologists and pathologists has proved help-ful to my group as we explore these issues. We are also fortunateas a field and as a profession that graduate students are keen tocontribute to the new mathematics of biology.

Acknowledgments

It is a pleasure to acknowledge the group members whocontributed to this work: Enrique T. Munoz, David J. Earl,

Vishal Gupta, Hao Zhou, Jun Sun, Ming Yang, and Jeong-ManPark. Support by the National Institutes of Health of research inmy group is gratefully acknowledged.

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Metabolic Engineering: Developing NewProducts and Processes by Constructing

Functioning Biosynthetic Pathwaysin vivoGregory Stephanopoulos and Kyle L. Jensen

Massachusetts Institute of Technology, Dept. of Chemical Engineering 77 Massachusetts Avenue, Cambridge, MA 02137

DOI 10.1002/aic.10725


Keywords: metabolic engineering, pathway engineering, cell engineering

In a recent AIChE Journal perspective on Metabolic Engi-neering1 we asked rhetorically whether the microbial worldis so diverse as to allow one to isolate some microbe

capable of producinganydesired molecule. It turns out that thisis very likely the case, a manifestation of the enormous diver-sity of molecules and reaction processes resident in a microbe.These actually constitute the mechanisms by which cellularfunctions are being carried out. The problem with most organ-isms is that they may make only traces of any single desiredmolecule and under conditions that may be difficult to imple-ment on an industrial scale. These microbes must be improvedbefore their potential is realized. Furthermore, after demon-strating that it is possible to cross the species barrier, pathways

that are incomplete for the production of a molecule in oneorganism can now be completed by transferring the missingpieces from another microbe. Thus, the enormous diversitypresent in an array of species can now be commandeered foraccomplishing a specific purpose, such as the production ofentirely new products or the construction of new synthesisroutes for existing products. This is the goal and essence ofmetabolic engineering.

Metabolic engineering was developed in the previous decadeto improve industrial strains using modern genetic tools. Whilemicroorganisms were modified before by random mutation andselection methods, the development of recombinant technolo-gies in early 80s allowed directedstrain modification by intro-

ducing specific genes conferring desirable properties to cellsfor industrial, medical and environmental applications. Meta-bolic engineering, thus, emerged as the scientific disciplineoccupied with the improvement of cellular properties throughintroduction to cells of specific transport, enzymatic or regu-latory reactions using, primarily, recombinant technologies.2,3

In less than a decade an impressive number of metabolicengineering applications have appeared in diverse areas includ-

ing aminoacid fermentations,4 polyketide and novel antibioticsynthesis,5 indigo and aromatic aminoacid synthesis in Esche-richia coli,6 golden rice,7 ethanologenic E. coli,8 isoprenoid(lycopene) overproduction,9 indene biocatalysis for the synthe-sis of chiral pharmaceuticals,10 tricistronic gene expression inChinese Hamster Ovary cells for foreign protein overproduc-tion under no growth and high viability conditions,11 manipu-lation of the glycosylation pathway in mammalian cells,12

1,3-propanediol and succinate production in E. coli as mono-mers for polymer production from renewable resources, andmany, many others along with numerous applications in themedical and environmental areas.13,14

Metabolic engineering makes extensive use of applied mo-

lecular biological methods in order to introduce pathway mod-ifications and controls at the genetic level. As such, its exper-imental implementation has a strong molecular orientation.However, metabolic engineering is much more than just anindustrial variant of genetic engineering. Since the goal is theoverproduction of a product, we must be concerned with thefunction of the entire pathway, as well as its optimal configu-ration in terms of adequate precursor supply and kinetic con-trols. This means that one needs to examine a broader biore-action network that extends beyond the strict collection ofthose reactions just necessary for product synthesis. For exam-ple, many biosynthetic pathways are net producers or consum-ers of energy (ATP) and reducing equivalents (NADH,

NADPH). These resources are produced and consumed bymany other reactions and for many functions in a cell. Theintroduction of a new pathway or the amplification of its rateshould be done in a way that does not disturb the cellularmolecules too far away from their normal (physiological)steady state. This means that proper consideration must begiven to the entire bioreaction network and this is the maindifferentiating characteristic of metabolic engineering: It con-cerns itself with a biosynthetic route in its entirety instead ofisolated cellular reactions.15 As mentioned, it is often necessaryto transfer some reactions from a different organism in order tocomplete a pathway. This opens many possibilities as to thepossible biosynthetic routes that may be used for product

*Correspondence concerning this article should be addressed to G. Stephanopoulosat [email protected].


Perspective



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synthesis.16 Some may be thermodynamically infeasible andsome others may incur particularly high costs in terms ofprecursor use or energetics. Finally, the ultimate carbon andenergy source(s) (glucose, oxygen, minerals, vitamins) must betransferred into the cell from the medium. The rate of reactantimport and, similarly product export, are important steps in theoverall process.

It is clear from the above simple outline of a cell factory that

its design, optimization and control make heavy use of theprinciples and methods of chemical engineering developed forthe design and operation of chemical plants. This is the basisfor the critical role of the discipline in the genesis and contin-ued growth of metabolic engineering.

While attention is often focused on pathway optimization,the importance of using the diversity of microorganisms fornew product synthesisshould not be underestimated. This canbe done either by introducing specific new enzymes (throughthe expression of their genes) in a cell, or by the introductionofenzyme libraries creating large diversities of entirely newmolecules from which those with desired properties must beselected. Efficient methods for creating large libraries along

with creative ideas for the selection of desired products arecritical elements in this approach.

Rational, or model-based, and combinatorial methods can beused in the design of optimal pathways.17 Rational approachesmake use primarily of stoichiometric approaches as stoichio-metric models are the only type of models that can be used withreasonable reliability on a cell-wide basis. Kinetic models arenot as useful because models of enzymatic kinetics that arevalid under intracellular conditions are rare. In addition, theregulation of these reactions at the transcriptional and enzy-matic levels is largely unknown. Combinatorial approaches,whereby a cell is transformed with random genomic librariesand well-defined mutants are selected, compliment the rationalapproaches. A key concept here is that of inverse metabolicengineering,18 whereby a desired mutant is selected from alibrary and then its specific genetic modification, typically genedeletion or overexpression, are well characterized. This is apowerful approach to identifying specific genes that materiallyimpact the product phenotype either by their stoichiometric,kinetic or (primarily) regulatory effects.

Biotechnological routes are presently preferable to chemicalones in the production of chiral pharmaceuticals and complexfine chemicals, in precision chemistry and addition of newfunctionalities to existing molecules, and in the utilization ofrenewable resources, all areas with high expected growth rate.Furthermore, various problems that impaired the developmentof biological processes in the past (such as low titer, product

inhibition, and slow rates) are rapidly being solved by a varietyof newly developed methods. For example, product inhibitionis minimized or altogether avoided by engineering enzymemutants resistant to high product levels, while osmo-tolerantstrains allow accumulation of continuously higher product con-centrations. Continued levels of strong R&D support by theU.S. Federal Government and industry will be creating anincreasing number of opportunities for biotechnological appli-cations. As a result of these developments, life sciences willimpact the chemical industry in a very profound way. Evidenceof this assertion is widespread: an approximate market of $60Bfor chiral pharmaceuticals; a robust and growing biotechnolog-ical industry (with more than $40B in sales and hundreds of

new products in the regulatory approval pipeline); and anincreasing number of biotechnologically produced productssuch as 1,3-propanediol, polylactic acid and an array of newbiopolymers. This trend is very likely to continue in the futureand metabolic engineering will be providing the enabling tech-nologies for harnessing the potential of microbes for an ex-panding portfolio of new applications.

So, why might chemical engineers be interested in metabolic

engineering? First, metabolic engineering combines the intel-lectual framework and implementation tools required to cap-ture the enormous potential of biology for industrial and med-ical applications. Its concepts and tools should be familiar tochemical engineers as metabolic engineering borrows heavilyfrom chemical reaction engineering. Second, the importance ofmetabolic engineering in materials, fuels, and specialty chem-icals (pharmaceuticals and chiral compounds) is undeniable asevidenced by a growing number of applications in these ar-eas.19 In the medical field, the greatest impact of metabolicengineering will be in the development of methods for therigorous assessment of the physiological state and determina-tion of reasonable enzymatic targets for the treatment of dis-

ease. This will be implemented either by direct therapeuticintervention or screening programs for the discovery of newdrugs. Finally, this is an excellent entry for chemical engineersinto a very rich field of scientific inquiry.20 Biological systemsowe their exceptional properties to specific chemical reactionscatalyzed by enzymes that, in a growing number of cases, canbe uniquely prescribed from genomic information. In otherwords, genomics provides the means to define the specific stepsof the chemical reaction system that can be subsequently ana-lyzed using the tools of metabolic engineering. This is a pro-found difference from typical chemical reacting systems wheredefining the actual reaction steps is a major challenge.

Chemical reactions are, for the most part, responsible for thewonders of biology. Metabolic engineering combines the toolsand concepts of reaction engineering and molecular biology forthe analysis and purposeful modification of bioreaction net-works.21 It also provides a framework for integrating andquantifying genomic information and cell-wide data generatedfrom modern technologies. As such, it is the natural vehicle forcapturing the enormous potential of biology and transformingit into the enabling science of many new industrial and medicalapplications. Chemical engineers are in a unique position toextend their educational and research paradigm into the mostexciting field of scientific inquiry. This will require that theyembrace biology as a foundational science equal to chemistryand modify the curriculum to reflect this fundamental changeinto chemical and biological engineering.

Acknowledgment

NSF award number: BES-0 331364.

Literature Cited

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3. Stephanopoulos G,Vallino JJ. Network rigidity and meta-



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Eng., 2003:5;32-41.5. Pfeifer BA, Admiraal SJ, Gramajo H, Cane DE, Khosla C.

Biosynthesis of complex polyketides in a metabolically

engineered strain of E-coli. Science. 2001:291;1790.6. Murdock D. Ensley BD, Serdar C, Thalen M. Construction

of metabolic operons catalyzing the de-novo biosynthesisof indigo in escherichia-coli. Biotechnol. N.Y., 1993:11;381.

7. Ye X. Al-Babili S, Kloti A, Zhang J, Lucca P, Beyer P,Potrykus I, Engineering the provitamin A (beta-carotene)biosynthetic pathway into (carotenoid-free) rice en-dosperm. Science. 2000:287;303.

8. Ingram LO, Aldrich HC, Borges ACC, Causey TB,. Mar-tinez A, Morales F, Saleh A, Underwood SA, Yomano LP,York SW, Zaldivar J, Zhou SD. Enteric bacterial catalysisfor fuel ethanol production.Biotechnol Prog.1999:15,855.

9. Farmer WR, Liao JC. Improving lycopene production inescherichia coli by engineering metabolic control. Nat

Biotechnol. 2000:18;533.10. Stafford DE, Yanagimachi KS, PA. Lessard, Rijhwani

SK,. Sinskey AJ, Stephanopoulos G. Optimizing biocon-version pathways through systems analysis and metabolicengineering. Proc Natl Acad Sci USA. 2002:99;1801.

11. Schlatter S. Bailey JE, Fussenegger M. Novel surfacetagging technology for selection of complex proliferation-controlled mammalian cell phenotypes. Biotechnol Bio-eng. 2001:75;597.

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Eppler S, Carroll K, Chamow S, Peers D, Berman P,Krummen L. Engineering Chinese hamster ovary cells tomaximize sialic acid content of recombinant glycoproteins.

Nat Biotechnol, 1999:17;1116.13. Yarmush DM, MacDonald AD, Foy BD, Berthiaume F,

Tompkins RG, Yarmush ML. Cutaneous burn injury altersrelative tricarboxylic acid cycle fluxes in rat liver. J of

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Moscow.2000:65;324.15. Stephanopoulos G, Sinskey AJ. Metabolic engineering:

Issues and methodologies.Trends in Biotechnology, 1993;11:392-396.

16. Mavrovouniotis M, Stephanopoulos Geo, StephanopoulosGr. Synthesis of biochemical production router. Comp inChem Eng.1992:16;605.

17. Alper H, Miyaoku K, Stephanopoulos G. Construction ofoverproducing E. coli strains by combining rational andcombinatorial gene knockout targets. Nature Biotechnol-

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2005:23;612-616.18. Yong-su Jin, H. Alper, Yang Y-T, Stephanopoulos G.

Improvement of xylose uptake and ethanol production inrecombinant Saccharomyces cerevisiae through inversemetabolic engineering approach.Applied and Environ. Mi-crobiology. (in press) 2005.

19. Stephanopoulos G, Kelleher J. How to make a superiorcell. Science, 2001:292:2024-2026.

20. Stephanopoulos G. Chemical and biological engineering.Chem Eng Sci.2003:58:3291-3293 and 58:4931-4933.

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Dimensional Analysis for Planetary Mixer:Modified Power and Reynolds Numbers

G. Delaplace, R. Guerin, and J. C. LeulietINRA-LGPTA, 59651 Villeneuve dAscq, France

DOI 10.1002/aic.10563

Published online August 29, 2005 in Wiley InterScience (www.interscience.wiley.com).

Mixing times, power consumption, heat transfer, and scale-up predictions in an agitated

vessel require the use of correlations between dimensionless groups such as Prandtl, Nusselt,Power, and Reynolds numbers. These dimensionless numbers are now well established for an

agitated vessel equipped with a vertically and centrally mounted impeller in the tank for both

Newtonian and non-Newtonian fluids. To our knowledge, there is more ambiguity as to the

definition of the characteristic speed and dimensions, which should be taken into account in

the dimensional analysis of planetary mixers. The aim of this paper is twofold: (1) to propose

modified Reynolds and Power numbers for planetary mixers and (2) to ascertain the reliability

of the modified dimensionless number proposed for a particular planetary mixer, The TRI-

AXE, which uses a combination of rotation and gyration of a pitched blade turbine to achieve

mixing. The modified Reynolds and Power numbers proposed involve the maximum tip speed

as characteristic velocity and are consistent with the definition of traditional Reynolds and

Power numbers when only a single revolution around the vertical axis of the mixing device

occurs in the vessel, as is the case for a standard mixing system. Experimental power

measurements carried out with a planetary mixer when mixing highly viscous Newtonian

fluids show that the modified Reynolds and Power numbers proposed succeed in obtaining a

unique power curve for the mixing system independently of the speed ratio. This close

agreement proves that the modified Reynolds and Power numbers are well adapted for

engineering purposes and can be used to compare the power-consumption performances of

planetary mixers with well-established technologies. 2005 American Institute of ChemicalEngineersAIChE J, 51: 30943100, 2005

Keywords: mixing, planetary mixers, dimensional analysis, power consumption,

Newto nian viscous fluids

Introduction

In the second half of the twentieth century, the systematic

use of dimensional analysis to investigate mixing processes has

allowed this field to evolve from arts into sciences. Today the

whole field of classical stirring technology (here, the word

classicalrefers to impellers vertically and centrally mounted in

the tank) has been examined, so that the definition of signifi-

cant dimensionless groups has now become well established.

Thus, for any stirring operation (heat transfer, blending, and so

on), depending on the flow regime and the mixing systems

investigated, numerous correlations involving various dimen-

sionless numbers have been proposed in the open literature for

both design and/or scale-up. Consequently, a deeper process

understanding and/or better or reproducible products can be

achieved. This is not yet the case for the planetary mixers.

Indeed, for this kind of mixing equipment, the literature is

relatively scarce.1-6 In addition, some dimensionless numbers

still suffer from ambiguity with respect to the characteristic

speed and dimension, which should be taken into account.

This lack prevents the comparison of performances of the

planetary mixers with those of classical mixing systems. For

Correspondence concerning this article should be addressed to G. Delaplace [email protected].


FLUIDMECHANICS AND TRANSPORT PHENOMENA



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example, the Reynolds number Re and Power number Np are

now well established for an agitated vessel equipped with

various geometries of impeller vertically and centrally mounted

in the tank for both Newtonian and non-Newtonian fluids. Npand Re are traditionally used to characterize the power de-

mands of a classical mixing system (Npvs.Re), when no vortex

formation occurs in the tank (the Froude number can be ne-

glected). In these dimensionless numbers, the characteristic

length chosen is the diameter of the impeller that, in fact,corresponds to an external dimension of the impeller perpen-

dicular to the vertical revolution axis. The characteristic veloc-

ity chosen (ND) is proportional to the maximum linear ve-locity encountered in the vessel (ND). Note that thecharacteristic velocity corresponds to the impeller tip speed

divided by .

However, for planetary mixers the maximum linear velocity

encountered in the vessel is influenced by both the relative and

displacement velocities and, consequently, depends on the two

revolution speeds. In the same way, the characteristic dimen-

sion of the mixing system is much more complex to define.

Therefore the classical Reynolds and Power numbers should be

adequately modified to take into account the complexity of thecombined motion required by the agitator.

The aim of this paper is twofold : (1) to propose modified

Reynolds and Power numbers for planetary mixers and (2) to

ascertain the reliability of the dimensionless numbers proposed

for a new planetary mixer, The TRIAXE system, which uses

a combination of rotation and gyration of a pitched blade

turbine to achieve mixing.

Experimental

Mixing equipment

The mixing equipment used in this investigation is the TRI-

AXE system (HOGNON S.A., Mormant, France), which

allows the agitator to combine two motions: gyration and

rotation (Figure 1). This planetary mixer is characterized by

two revolutionary motions that are nearly perpendicular. Gy-

ration is a revolution of the agitator around a vertical axis,

whereas rotation is a revolution of the agitator around a nearly

horizontal axis. These double motions allow the agitator to

periodically come in contact with the entire volume of the

vessel. In this work, the mixing tool for the TRIAXE system

is a four pitched blade turbine (Figure 2). The tank used is a

transparent glass cylinder with rounded bottom (Figure 2). The

diameter of the vessel is 0.4 m. In this work, experimental

measurements were carried out when the agitator was fully

immersed in the liquid. This liquid height corresponds to a

liquid volume of 38 L, corresponding to a liquid height of 0.39m.

The mixing equipment was driven by two variable-speed

motors. To obtain the total power consumption of the TRI-

AXE system, power draw measurements were carried out

alternately for the two variable-speed drive motors that control

the impeller revolutions. To do so, a torque meter (Scaime Inc.,

Annemasse Cedex, France) ranging from 0 to 5 Nm, was

mounted alternately on the two motor drive shafts (Figure 2)

and the torque was measured for various impeller speed ratios.

Total power draw was estimated as a simple summation of the

two motor drives. More exactly, the procedure to obtain power

requirement of each motor was the following:

(1) The torquemeter is mounted on one of the two motor

drive shafts just before the reduction gearbox. The reduction

gearbox ratio RG for the gyration motor drive is equal to 145.

The reduction gearbox ratio RR for the rotation motor drive is

equal to 34.

(2) The revolution speed of the motor drive shaft that is not

equipped with the torque meter is maintained constant, whereas

torque measurements exerted on the second motor drive shaft

(MG motor or MR motor, respectively) are performed for various

revolution speeds of the second motor drive shaft (NG motoror

NR motor, respectively). This was done both when mixing a

Newtonian fluid (MG motororMR motor, respectively) or when air

(no loading) was contained in the vessel (MG0motororMR0motor,

respectively), to determine the effective torque exerted on each

motor drive shaft [(MG motor MG0motor) o r (MR motor MR0motor), respectively].

(3) Torque measurements were carried out on the full range

of speeds available on the motor drive shafts. Because of the

gearbox reductions on the two motor drive shafts, the range of

revolution speeds available for the two agitator shafts (after the

gearbox) are: 0 to 16 rpm for NG and 0 to 90 rpm for NR.

(4) Then neglecting mechanical friction in the gear box, theeffective torque required by each agitator shaft was plotted:

(MG MG0) (MG motor MG0motor)RG or (MR MR0) (MR motor MR0 motor)RR, respectively, as a function of theagitator speeds (respectivelyNG or NR). At this step, we have

observed that effective torque values exerted on rotation agi-

tator shaft were not dependent on the gyrational speed of the

impeller (see Figure 3 as an example) and vice versa. Conse-

quently, the effective torque values exerted on rotation agitator

shaft (respectively on gyration agitator shaft) can be predicted

by the only knowledge of viscosity and rotational impeller

speed: MR MR0 1.265NR (respectively MG MG0 1.595NG). Note that, for a fixed revolution speed and the

Figure 1. TRIAXE system.

For the planetary mixer studied, ds 0.14 m andD 0.38 m.



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TRIAXE

system under investigation, the torque exerted ongyration agitator shaft is the same order as that obtained for

rotation agitator shaft. The same observation was already made

and detailed in a previous paper7 when the agitator was not

fully immersed in the liquid. Then, the power input for each

motor can be deduced. Power attributed to gyration and rota-

tion are, respectively, PG (MG motor MG0motor)2NG motorandPR (MR motor MR0motor)2NR motor, whereNG motorand

NR motorare, respectively, the gyrational and rotational speeds

of the motor shaft. Finally, total power consumption P can be

estimated by adding the contribution of power draw required

by the two motors (PG PR).(5) Using this procedure, the total power consumption of the

planetary mixer when mixing a Newtonian fluid ( 22 Pasand 1400 kg/m3) was plotted in Figures 8 and 9 (seebelow).

Agitated fluid

The agitated fluid is a highly viscous Newtonian fluid. The

liquid consists of glucose syrup/water mixtures of various

viscosities ranging from 15 to 29 Pas, depending on the

temperature encountered in the vessel. The rheological prop-

erties and densities of the test fluid were obtained at the same

temperatures as those encountered in the mixing equipment.

Density at 20C of the test fluid is 1400 kg/m3. The rheological

properties of the test fluid were measured in standard controlled

rotational speed concentric cylinders (Rheomat 30, Contraves

AG, Zurich, Switzerland). The shear rate range applied to the

controlled shear rate viscosimeter varied from 0 to 500 s1and

corresponds to the shear rate range encountered in the tank.

Theory

Dimensional analysis for an agitated vessel equippedwith an impeller vertically and centrally mounted in the

tank

When mixing Newtonian liquids in an agitated vessel with-

out baffles, equipped with an impeller vertically and centrally

mounted in the tank (Figure 4), the power P of a given stirrer

type and given installation conditions (vessel diameter T, agi-

tator height H, liquid height HL, and bottom clearance C) in a

homogeneous liquid depends on the agitator diameter d(as the

characteristic length), the material parameters of the liquid

Figure 2. Picture of the agitator and vessel of the TRI-

AXE system used in this investigation.

Red circle on the picture refers to the torquemeter device. Thevessel tank diameter Tand liquid height HLwere set equal to0.4 and 0.39 m, respectively. For the planetary mixer studied,ds 0.14 m and D 0.38 m.

Figure 3. Effective torque exerted on rotation/ vs. im-

peller rotational speed.

Symbols refer to various impeller gyrational speeds tested.Solid line is obtained by linear regression.

Figure 4. Classical geometric parameters and notations

used for mixing vessel equipped with an im-

peller vertically and centrally mounted in the

tank.



16/229

(density and dynamic viscosity ), and on the stirrer speedN.

When no vortex exists, the acceleration attributed to gravity g

is not relevant with respect to the power draw.

The above-mentioned dependency on dimensional parame-

ters

F1P, d, T, H, HL, C, , , N 0 (1)

leads, by way of dimensional analysis, to the following

dependency between dimensionless numbers8:

F2Np, Re,T/d,H/d,HL/d,C/d 0 (2)

Np P/N3d5 is the so-called Newton number (often termed

thePower number) and Re Nd2/is the Reynolds number.For a given agitator and fixed installation conditions, Eq. 2

is reduced to a dependency between Np and Re.

F3Np, Re 0 (3)

Dimensional analysis of a planetary mixer

Assuming that the acceleration arising from gravity (as in the

previous case) does not influence the mixing process of highlyviscous fluids, the list of relevant dimensional parameters in-

fluencing the power consumption, when mixing Newtonian

liquids with the TRIAXE system equipped with a pitched

blade turbine, is

F4P, D, ds, , , NR, NG, installation conditions 0

(4)

In Eq. 4, NR and NG are, respectively, the rotational and the

gyrational impeller speeds;D and ds are the geometric param-

eters reported in Figure 5. and are, respectively, the density

and dynamic viscosity of the liquid. The installation conditions

refer here to the vessel diameter T, the liquid heightHL, and the

bottom clearance C.

For fixed installation conditions, this seven-parameter di-

mensional space leads to a power characteristic consisting of

four pi-numbers

F5NpG, ReG,NR

NG,D

ds 0 (5)where Np

G P/NG

3 ds5 and ReG NGds

2/.

For a given planetary system, the ratio D/ds is fixed and the

power characteristic is reduced to a mutual dependency be-

tween each of the following three parameters constituting the

pi-set

F6NpG, ReG, NRNG 0 (6)

Note that in Eqs. 5 and 6 the characteristic length and

velocity that appear in the modified power NpG and ReynoldsReGnumbers aredsand NGds, respectively. This was chosen at

first approximation, given that when no rotational motion oc-

curs (NR 0), the planetary mixer under investigatiom istransformed to a classical mixing system (Figure 6). Using

symbols adopted for classical mixing systems, ds, D, and NG(Figure 6) become, respectively, equal to d, H, and N (Figure

4). Thus, modified power NpG

and Reynolds ReG numbers

transform to the well-known Np and Re traditionally used for

classical mixing systems.

A closer look at Eq. 4 facilitates a reduction in the number

of physical quantities in the list of relevant parameters. Indeed,

it is possible to introduce as a characteristic velocityucha value

that is proportional to the impeller tip speed and reduce the list

of relevant physical variables describing the problem by three

parameters: NR, NG, and D:

F7P, ds, , , uch, installation conditions 0 (7)

Figure 6. Analogies between the geometric parameters

of the classical mixing system and the TRI-

AXE planetary mixer when rotational speed is

set at zero.

Figure 5. Sketch and symbols used for the TRIAXE sys-tem.



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For fixed installation conditions and a given planetary system(D/dsis known), this five-parameter dimensional space leads to

a power characteristic consisting of only two pi-numbers

F8Npm, Rem 0 (8)

with Npm

P/uch3 ds

2 and Rem uchds/.Note that for a planetary mixer, the instantaneous impeller

tip speed uimpeller tip(t) in an inert reference frame, is not a

constant value with time t. This will be shown and discussed

later. By analogy with a dimensional analysis for classical

mixing systems, the characteristic velocity chosen in Eq. 8 was

the maximum velocity encountered in the vessel divided by

uch maxuimpeller tipt/ (9)

To sum up, the dimensional analysis of the power consump-

tion of the TRIAXE system in a fixed installation condition

when mixing highly viscous fluids, leads either to a relation-

ship between three pi-numbers (Eq. 6) or two pi-numbers (Eq.

8) if a characteristic speed proportional to the maximum im-

peller tip speed is introduced in the parametric dimensional

space. In addition, it has been shown that the pi-numbers can be

reduced to well-known Reynolds and Power numbers, when

the rotational speed is zero. This is quite logical because, in this

case, the TRIAXE system is transformed to a classical mixing

system equipped with an agitator vertically and centrally

mounted in the tank.

In the following section, the way to compute the character-

istic speed for the TRIAXE system will be detailed. Then, the

reliability of the two pi-numbers proposed will be ascertained,

using power consumption measurements.

Determination of the characteristic speed of theTRIAXE system

For the TRIAXE system, which combines the dual motions

reported in Figure 1, the magnitude of instantaneous impeller

tip speed in an inert reference frame is defined as follows (more

details are given in Appendix A)

u impeller tipt 2NR D22

2NG ds22

2NG D22

cos22NRt 22NRNGdsDsin2NRt

1/ 2

(10)

where NR and NG are, respectively, the rotational and thegyrational impeller speeds;D and ds are the geometric param-

eters reported in Figure 1; and trepresents the time.

Depending on whether the ratio NRds/NGd is 1 (see Ap-pendix B), the function t x uimpeller tip(t) does not have the

same evolution with time and reaches two (NRds/NGd 1) orfour extrema (NRds/NGd 1). The various shapes of theabsolute impeller tip speed with time are illustrated in Figure 7.

The derivation of Eq. 10 allows us to obtain the instants for

which the magnitude of absolute impeller tip speed reaches

extrema (see Appendix B), and thus to compute the maximum

value for impeller tip speed max[uimpeller tip(t)]. Finally, using

Eq. 9, uch can be deduced.

Results and Discussion

Power consumption measurements obtained for the TRIAXE

system investigated when mixing a Newtonian fluid are shown in

Figure 8. Results are presented in terms of the dimensionless

numbers (NpG

vs. ReG) previously defined in Eq. 6.

Figure 8 clearly shows that the power characteristic of the

TRIAXE system cannot be reduced to a unique relation

between Power and Reynolds numbers when ds and NGds are

used as characteristic length and velocity, respectively. Indeed

in this case, it would appear that the power data are strongly

influenced by the speed ratio values NR/NG.

In contrast, it is shown in Figure 9 that the use of modified

Reynolds and Power numbers, such as those suggested in Eq.

8, succeed in obtaining a unique power characteristic for the

TRIAXE system, independently of the speed ratios chosen.

This proves to a certain extent the reliability of using maximum

impeller tip speed as characteristic velocity and a dimension

perpendicular to the vertical axis of revolution as characteristic

length. Moreover, it can be observed from Figure 9 that the

product Npm

Rem is constant, as obtained with classical mixing

systems when mixing highly viscous fluids. The value of the

product was found to be 343. As with classical mixing equip-

Figure 7. Example of evolution with time of the absolute

impeller tip speed.

For the two symbols, D 0.38 m and ds 0.14 m. For theblack symbols, NR and NG were set at 0.286 and 0.1 rev/s,respectively. For the gray symbols, NR and NG were set at0.286 and 0.345 rev/s, respectively.

Figure 8. Power characteristics of the planetary mixer

using the three pi-numbers defined in Eq. 6.



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ments, these results allow a Reynolds number to be defined and

the power consumption of the planetary mixer to be predicted,

on the basis of the two impeller revolution speeds (gyration and

rotation) and the liquid properties. It should be noted that a

product Npm

Rem of 343, does not mean that the power con-sumption of the planetary mixer is fairly similar to that of the

helical ribbon impeller (NpRe around 300 for standard helical

ribbon9). Indeed, for a given liquid under a laminar regime,

power consumption is obtained not only by multiplying the

power constant NpRe, but also by the characteristic length

exponent 3. In this case, to include the same tank volume, the

characteristic length required for the helical ribbon is around

twofold higher than that of the planetary mixer under investi-

gation. Consequently, the power draw required by the TRI-

AXE system is lower than that by standard helical ribbon

impeller.

ConclusionIn this paper, modified Reynolds and Power numbers for a

planetary mixerthe TRIAXE system, which combines dual

revolutionary motionshas been developed.

It has been shown that the proposed modified Reynolds and

Power numbers, which involve the maximum impeller tip

speed as characteristic velocity and a dimension perpendicular

to the vertical axis of revolution as characteristic length, allow

one to obtain a unique power characteristic of the mixing

system, regardless of the speed ratios. Moreover, the charac-

teristic length and velocity chosen ensure that the modified

dimensionless numbers proposed are consistent with the defi-

nition of traditional Reynolds and Power numbers, when the

impeller performed only a single revolution around the verticalaxis in the tank, as in the case of a classical mixing system. So,

it clearly appeared that the modified Reynolds and Power

numbers can be easily used to compare the power consumption

of planetary mixers with that of conventional mixing systems.

In our judgment, the suggested modified Power and Reyn-

olds numbers can be used for other planetary mixers that

combine two revolutions around a vertical axis. Only the

expression of the characteristic velocity must be modified, to

allow for the differing operating conditions. In contrast to

double-armed planetary mixers or twin-blade arrangement, di-

mensional analysis defined in Eq. 6 should be preferred be-

cause there is no way to reduce the pi-numbers using a char-

acteristic velocity that takes into account the two different

revolutionary speeds.

Acknowledgments

The authors are grateful to F. Brisard and J. F. Dauphin for valuablework in obtaining the experimental data and figures presented here.

Literature Cited

1. Tanguy PA, Bertrand F, Labrie R, Brito de la Fuente E. Numericalmodelling of the mixing of viscoplastic slurries in a twin bladeplanetary mixer. Trans IChemE 1996;74:499-504.

2. Tanguy PA, Thibault F, Dubois C, At-Kadi A. Mixing hydrodynamicsin a double planetary mixer. Trans IChemE. 199;77:318-323.

3. Landin M, York P, Cliff MJ, Rowe RC. Scaleup of a pharmaceuticalgranulation in planetary mixers.Pharm Dev Technol. 1999;4:145-150.

4. Zhou G, Tanguy PA, Dubois C. Power consumption in a doubleplanetary mixer with non-Newtonian and viscoelastic material. Trans

IChemE. 2000;78:445-453.5. Jongen T. Characterization of batch mixers using numerical flow

simulations.AIChE J. 2000;46:2140-2150.6. Delaplace G, Bouvier L, Moreau A, Guerin R, Leuliet J-C. Determi-

nation of mixing time by colourimetric diagnosisApplication to anew mixing system. Exp Fluids. 2004;36:437-443.7. Delaplace G, Guerin R, Bouvier L, Moreau A, Leuliet J-C. Perfor-

mances of a novel mixing device: The TRIAXE systemMixingtimes and power consumption for highly viscous fluids.Proceedings ofthe 11th European Conference on Mixing, Bamberg, Germany. Dus-seldorf, Germany: VDIGVC; 2003:589-596.

8. Zlokarnik M. Stirring Theory and Practice. Weinheim, Germany:WileyVCH Verlag; 2001.

9. Delaplace G, Leuliet J-C, Relandeau V. Circulation and mixing timesfor helical ribbon impeller: Review and experiments. Exp Fluids.2000;28:170-182.

Appendix A Scheme 1

Considering M to be a point located at the TRIAXE im-

peller tip, the absolute velocity ofMin the rotating reference

frame (ex, ey, ez) is given by

Va dO Mdt

R

dO Odt

R

dOMdt

R

dO Odt

R

dO Odt

R

O O with R/R

Scheme 1.

Figure 9. Power characteristic of the planetary mixer

using the two pi-numbers defined in Eq. 8.



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dO Odt

R

0 and OO

02NG0

00 ds/ 2

2NGds/ 200

dOMdt

R

dO Mdt

R

OM

with R/R

OM D/ 2cos2NRtD/ 2sin2NRt0

dOMdt

R

D/ 22NRsin2NRtD/ 22NRcos2NRt0

OM

02NG0

D/ 2cos2NRtD/ 2sin2NRt 0

002NGD/ 2cos2NRt

Va D/ 22NRsin2NRt 2NGds/ 2

D/ 22NRcos2NRt

2NGD/ 2cos2NRt

Consequently, the absolute velocity ofMin the inert reference

frame (X , Y , Z) is given by

Va D/ 22NRsin2NRt 2NGds/ 2sin2NGt 2NGD/ 2cos2NRtcos2NGt

D/ 22NRsin2NRt 2NGds/ 2cos2NGt 2NGD/ 2cos2NRtsin2NGt

D/ 22NRcos2NRt

Thus, the magnitude of absolute velocity ofMis given by

Va u impeller tipt D/ 22NR2 2NGds/ 2

2 2D/ 22NR2NGds/ 2sin2NRt

2NGD/ 22cos22NRt

Appendix B

It can be shown that the functiont x uimpeller tip(t), defined in

Eq. 10, reaches an extremum when the derivative of the function

t x w(t) is equal to zero with w(t) given by w(t) 2(D/2)2NR2NG(ds/2)sin(2NRt) [2NG(D/2)]

2cos2(2NRt).

The derivative of the function t x w(t) is dw(t)/dt 2NRcos(2NRt){[2(D/2)2NR2NG(ds/2)] 2[2NG(D/2)]2sin(2NRt)}.

Consequently dw(t)/dt 0 when the following conditionsapply:

t1

4NR

t 34NR

sin2NRt NRds

NGd

So, depending on whether ratio NRds/NGdis 1, functiontxuimpeller tip(t) has two or four extrema that are respectively

reached at

t 14NR,3

4NR

or at

t 14NR,3

4NR

or

arcsinNRds

NGd,

arcsinNRds

NGdFrom these extrema, a maximum value for impeller tip speed

max[uimpeller tip(t)] can be selected.

Manuscript received July 7, 2004, and revision received Apr

aiche_journal__vol[1]._51__no._12___december_2005_

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